An optimal combustion phasing leads to a high combustion efficiency and low carbon emissions in diesel engines. With the increasing complexity of diesel engines, model-based control of combustion phasing is becoming indispensable, but precise prediction of combustion phasing is required for such strategies. Since cylinder-to-cylinder variations in combustion can be more significant with advanced combustion techniques, this work focuses on developing a control-oriented combustion phasing model that can be leveraged to provide cylinder-specific estimates. The pressure and temperature of the intake gas reaching each cylinder are predicted by a semi-empirical model and the coefficients of this intake pressure and temperature model are varied from cylinder-to-cylinder. A knock integral model is leveraged to estimate the SOC (start of combustion) and the burn duration is predicted as a function of EGR fraction, equivalence ratio of fuel and residual gas fraction in a burn duration model. After that, a Wiebe function is utilized to estimate CA50 (crank angle at 50% mass of fuel has burned). This cylinder-specific combustion phasing prediction model is calibrated and validated across a variety of operating conditions. A large range of EGR fraction and fuel equivalence ratio were tested in these simulations including EGR levels from 0 to 50%, and equivalence ratios from 0.5 to 0.9. The results show that the combustion phasing prediction model can estimate CA50 with an uncertainty of ±0.5 crank angle degree in all six cylinders. The impact of measurement errors on the accuracy of the prediction model is also discussed in this paper.

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